Some preferred embodiments of the present invention address the diffraction-limited resolution in a remote-sensor optical system with an optical axis 11 (FIG. 1), and with a collimated beam 12 passing through an afocal lens 13 (having a magnification ratio of Z to 1) to form a magnified or minified beam 14 that reaches a MEMS scan-mirror array 15. The array in turn produces from that beam 14 a deflected beam 16 which next reaches a reimaging lens 17.
This lens in turn forms from the deflected beam a focused beam 18, at an image plane 19 spaced from the reimager by that element's focal length f. When the input beam 12 is on-axis as shown, the MEMS mirrors in the array 15 are necessarily set to be nominally planar, as a group—that is, all substantially aligned with a common base plane 38 of the array (or a common plane 38 of the mirror pivots).
In this on-axis, planar condition all the light 12, 14 that is coherent initially—before reflection by the MEMS scan-mirror array—is again coherent at each position 16 and 18, as well as the image plane 19, after the reflection. In other words, light that is all in phase initially is also all in phase later.
Furthermore with the MEMS mirrors in this condition they behave, for purposes of diffraction analysis, very much as if they were a single mirror having the overall size of the array. Accordingly the resulting diffraction-limited spot size φ, at the image plane 19 after passage of the beam 16, 18 through the reimaging lens 17, is inversely proportional to the size of that effective “single” mirror, which is to say the size of the array.
If there are N mirrors, each of size D, along one dimension of the array, then the size of the effective single mirror is the product ND, and the smallest spot size φ is inversely proportional to ND:
  ϕ  =                    2.44        ⁢        λ            ND        .  In this case, e. g. for an array of just two mirrors each having dimension D, that size is 2D.
  ϕ  =                    2.44        ⁢        λ                    2        ⁢        D              =          1.      ⁢      .22      ⁢              λ        /                  D          .                    
Thus for this on-axis, planar case, the diffraction-controlling dimension ND is twice the linear dimension D of each individual mirror. Thus the diffraction limit is twice as fine as (i. e. is half the size of) the spot size which corresponds to that dimension D of each individual mirror.
This condition may be regarded as characterizing sensed beams that are addressing field sources which are on axis (e. g., normal) with respect to the MEMS mirror array—or more generally whenever the individual mirror surfaces as a group are aligned with their common base plane. It will shortly be seen that a like condition applies to projected beams that are addressing field transmission targets, provided only that the beam outside the system is on axis and the array in its aligned, groupwise-planar condition.
What is of particular interest, however, is what happens to the diffraction limit if the external beam is off axis, and the MEMS array accordingly rotated out of its planar condition. This occurs as soon as the afocal MEMS beam steering system is dynamically modified—by rotation of the MEMS array 15—as this action does indeed correspond to operation with both the excitation beam 112 (FIG. 2) and the resulting magnified or minified beam 114 off-axis.
Under these conditions the light waves no longer in effect encounter (or “see”) the equivalent of a single mirror of linear dimension ND but instead encounter plural single mirrors whose extent is not combined. Diffraction then proceeds in accordance with the dimension D of only one individual MEMS mirror, so that the two subbeams 116 from adjacent mirrors have a phase difference 2Δ and the reimaged beam 118 has an enlarged (coarser) minimum spot size 119.
Thus the above-explained advantageous finer diffraction limit is unfortunately lost, and the applicable value is instead:
  ϕ  =                    2.44        ⁢        λ                    1        ⁢        D              =                            2.44          ⁢          λ                D            =              2.44        ⁢                  λ          /                      D            .                              
Analogously of interest, as already mentioned above, is the resolution of a coherent-beam (most typically laser) projection system (FIG. 3), in which a collimated projection beam 21 is deflected by a MEMS scan-mirror array 22 to direct plural individual beams 23 toward an afocal lens 24 (again with Z-to-1 magnification). Here the deflected beams 23 are on-axis (i. e., parallel to the optical axis 26)—and thereby producing, at the lens 24, an on-axis projected beam 25.
Here it is the beam divergence α that is controlled by the overall dimension of the mirror array 22, provided that the mirrors are in fact groupwise planar to yield an on-axis beam 25. In this favorable condition, the divergence is controlled by the product ND as before:
  α  =                    2.44        ⁢        λ            ND        =                            2.44          ⁢          λ                          2          ⁢          D                    =              1.22        ⁢                  λ          /                      D            .                              and for the simple exemplary case of two mirrors this reduces as before to—
  α  =                    2.44        ⁢        λ                    1        ⁢        D              =                            2.44          ⁢          λ                D            =              2.44        ⁢                  λ          /                      D            .                              
Again, however, the particular phenomenon of interest is the coarser diffraction limit corresponding to the dimension D of one individual MEMS mirror, when the system is modified (simply by rotation of the MEMS array) to operate with a phase difference 2Δ between the two deflected subbeams 123 (FIG. 4) entering the afocal lens 24, and with the projected beam 125 off-axis:
  α  =                    2.44        ⁢        λ            ND        .  
Thus, summarizing, when the AMBS system either images or projects to a different field location (FIGS. 2 and 4), unfortunately there arises in the wavefront a phase difference of 2Δ, where Δ=D sin θ—in which θ is the MEMS scan angle. This delay is proportional (for small θ) to the MEMS scan angle. Now the diffraction-limited spot size or divergence is set by the size of an individual MEMS mirror D, rather than the size of the entire N-mirror array and the corresponding product ND as before.
In a practical case the number N of individual mirrors is typically at least ten and sometimes on the order of a hundred. Consequently the adverse implications of this effect are very severe.
The described diffraction-limit-degrading effect is significant only if phase mismatch between adjacent mirrors departs from an integral number of wavelengths by roughly a tenth of one wavelength or more. In other words, if the total phase difference exceeds about 10% of a wave, diffraction in a sensor system is controlled by the individual mirror dimension. When the phase difference increases beyond about 90% of a wave, however, then once again the diffraction is controlled by the overall array dimension—until again the difference exceeds 110% of a wave.
As to the exact size of the diffraction-limited spot, the introductory discussion here is not rigorous but may be regarded as a first-order approximation. In particular the mirror scan angle θ causes the diffraction limit to be either λ/D or λ/ND multiplied by some theoretical form-factor; and what is of interest is the basic phenomenon—particularly the dominant effect of N—rather than that form-factor.
Analogously, a projection system illustrated in FIG. 3—projecting parallel to the system axis—has a beam divergence α, inversely proportional to the MEMS array size. When projecting to another field location, the identical optical system suffers a phase difference 2Δ, between adjacent MEMS rows, proportional to the MEMS scan angle θ—and the beam divergence is then inversely proportional to the individual MEMS mirror size D (FIG. 4).
In the case of such a projection system, if the phase difference can be maintained such that it is an integral number of wavelengths λ, then the system when operating at a single wavelength λ or over a narrow band about that wavelength can obtain imaging performance determined by the dimension of the entire scan-mirror array, not the individual mirrors. This provides a significant improvement over what would be possible in terms of the beam divergence of a projection system—in the cases being considered, again, factors of ten to one hundred.
To recapitulate, a potential shortfall in sharpness—with a MEMS scan-mirror array—develops from the phase error introduced by the arrangement of the mirrors. This phase error very undesirably forces the diffraction limit to scale with the area of each individual mirror, rather than the total area of the mirrors in the array.
As can be now understood, the prior art—although providing powerful and very sophisticated imaging and sensing capabilities—has left some refinements to be desired in the area of ideally fine-focused images and optical projection.